## Abstract

We suggest in this letter a new Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-reaction equations where the random walk is living both on the randomly walking spheres and inside the relevant balls. The method is mesh free both in space and time, and is well applied to solve high-dimensional problems with complicated domains. The algorithms are based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for balls and spheres. They can be conveniently used not only for the solutions, but also for a direct calculation of fluxes to any part of the boundary without calculating the whole solution in the domain. Some applications to exciton flux calculations in the diffusion imaging method in semiconductors are discussed. (C) 2018 Elsevier Ltd. All rights reserved.

Original language | English |
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Pages (from-to) | 141-148 |

Number of pages | 8 |

Journal | Applied Mathematics Letters |

Volume | 88 |

DOIs | |

Publication status | Published - 1 Feb 2019 |

## Keywords

- A system of diffusion–reaction equations
- Cathodoluminescence imaging of dislocations
- First passage time
- Random walk on spheres and balls
- A system of diffusion-reaction equations